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Forecasting the occurrence of debris flows is fundamental for issuing hazard warnings, and often focuses on rainfall as a triggering agent and on the use of empirical rainfall thresholds based on rain gauge observations. A recognized component of the uncertainty associated with the use of rainfall thresholds is related to the sampling of strongly varying rainfall variability with sparse rain gauge networks. In this work we examine the spatial distribution of rainfall depth in areas up to 10 km from the debris flow initiation points as a function of return period, and we exploit this information to analyze the errors expected in the estimation of debris flow triggering rainfall when rain gauge data are used. In particular, we investigate the impact of rain gauge density and of the use of different interpolation methods. High-resolution, adjusted radar rainfall estimates, representing the best available spatially-distributed rainfall estimates at the debris flows initiation point and in the surrounding area, are sampled by stochastically generated rain gauge networks characterized by varying densities. Debris flow triggering rainfall is estimated by means of three rainfall interpolation methods: nearest neighbor, inverse distance weighting and ordinary kriging. On average, triggering rainfall shows a local peak corresponding to the debris flow initiation point, with a decay of rainfall with distance which increases with the return period of the triggering rainfall. Interpolation of the stochastically generated rain gauge measurements leads to an underestimation of the triggering rainfall that, irrespective of the interpolation methods, increases with the return period and decreases with the rain gauge density. For small return period events and high rain gauge density, the differences among the methods are minor. With increasing the return period and decreasing the rain gauge density, the nearest neighbor method is less biased, because it makes use only of the closest rain gauge to the debris flow initiation point. On the contrary, inverse distance weighting and ordinary kriging, which are using rain gauges located farther from the debris flows in addition to the closest one, exhibit negative biases that increase with return period. The standard deviation of the interpolated values is larger when the nearest neighbor is used with respect to inverse distance weighting and ordinary kriging. For large return period and low rain gauge density, the differences among the methods are minor. [ABSTRACT FROM AUTHOR]